Full Idea
In 'constant domain' semantics, the domain of each possible world is the same as every other; in 'varying domain' semantics, the domains need not coincide, or even overlap.
Gist of Idea
A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.93